Finding an Optimal Region in One- and Two-Dimensional Arrays

Naoki KATOH  

IEICE TRANSACTIONS on Information and Systems   Vol.E83-D    No.3    pp.438-446
Publication Date: 2000/03/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: INVITED SURVEY PAPER
Category: Algorithms for Geometric Problems
optimal interval,  combinatorial optimization,  interclass variance,  image segmentation,  data mining,  

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Given N real weights w1, w2, . . . , wN stored in one-dimensional array, we consider the problem for finding an optimal interval I [1, N] under certain criteria. We shall review efficient algorithms developed for solving such problems under several optimality criteria. This problem can be naturally extended to two-dimensional case. Namely, given a NN two-dimensional array of N2 reals, the problem seeks to find a subregion of the array (e. g. , rectangular subarray R) that optimizes a certain objective function. We shall also review several algorithms for such problems. We shall also mention applications of these problems to region segmentation in image processing and to data mining.

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